a matrix $pintextmd{c}^{ntimes n}$ is called a generalized reflection matrix if $p^{h}=p$ and $p^{2}=i$‎. ‎an $ntimes n$‎ ‎complex matrix $a$ is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix $p$ if $a=pap$ ($a=-pap$)‎. ‎in this paper‎, ‎we introduce two iterative methods for solving the pair of matrix equations $axb=c$ and $dxe=f$ over reflexiv...

The matrix pencil algebraic characterisation of the families of invariant subspaces of an implicit system S(F, G) : Fz = Gz F, G € K m x n , is further developed by using tools from Exterior Algebra and in particular the Grassmann Representative g(V) of the subspace V of the domain of (F,G). Two different approaches are considered: The first is based on the compound of the pencil C'd(sF — G), w...

We consider tilings of a rectangle of size n×k with square tiles of size 1×1 and 2×2. We present a method to calculate the number of such tilings via matrix multiplication, where we optimize the number of multiplications needed and reduce the space required for the matrix multiplication by dynamically generating the matrices involved.

Let X and Y be two sequence spaces and A = (ank) be an infinite matrix. If for each x ∈ X the series An(x) = ∑∞ k=0 ankxk converges for each n and the sequence Ax = (Anx) ∈ Y we say that the matrix A maps X into Y . By (X,Y ) we denote the set of all matrices which map X into Y . Let c be the set of all convergent sequences. A matrix A is called regular if A ∈ (c, c) and limn→∞Anx = limk→∞ xk f...

We show that there are two reasons why the partial width for the transition 1ð ð3SÞ ! þ b1ð1PÞÞ is suppressed. First, the spin-averaged matrix element Ið3Sjrj1PJÞ is small, being equal to 0:023 GeV 1 in our relativistic calculations. Secondly, the spin-orbit splittings produce relatively large contributions, giving Ið3Sjrj1P2Þ 1⁄4 0:066 GeV , while due to a large cancellation the matrix element...

In 1853 Hamilton showed that a general linear vector transformation in three dimensions satisfied a third-order equation. In this paper we indicate how Hamilton came to consider this transformation and what he did with it. Hamilton’s work was written in the language of quaternions, which he invented. We describe this work using vectors instead of the quaternions. In addition, we express Hamilto...

An alternative to the matrix inverse procedure is presented. Given a bit register which is arbitrarily large, the matrix inverse to an arbitrarily large matrix can be peformed in O(N 2) operations, and to matrix multiplication on a vector in O(N).

Understanding the pattern of gluon radiation in tt̄ production processes is important for making an accurate determination of the top mass from the measurement of its decay products. In a recent paper we showed that the exact matrix element and parton shower (HERWIG) calculations gave very different results for the distribution of gluon jets in tt̄ production at the Tevatron pp̄ collider. By repea...